He really doesn't want to sit still!
Maybe he is a kinesthetic learner?
Not everyone learns the same way, if his natural preference is to learn kinesthetically then encouraging him to sit still or stay on your knee whilst you read would be pointless and possibly detrimental to future interest in learning. Maybe look into it? Kinesthetic learners can usually do two things at once (listen to the story - may even occasionally glance at the page to see the picture - and build blocks/dance/roll cars down a ramp at the same time), it doesn't mean they are not listening or are ignoring you or the book. The physical movement helps them to take in information so for example later in life being allowed to squeeze a soft ball at their school desk could help them to take in an oral lecture. These sorts of learners can sometimes be accused by teachers of messing around, not listening and not paying attention etc because they are constantly fiddling with the contents of their pencil case. In fact the fiddling helps them retain the information they are hearing and can even cue recall in exam situations.
I would be open to the idea and look out for it in other areas as it would be helpful to know this so you can speak to his teachers in the future etc.
OK, lecture on learning styles over.
My DS loves books, always has since he was a newborn but there is no way on this earth he would read a book at BT. We have a slow dance at BT (I used to sing, now we have a CD playing), so a calm down and cuddle for 3 mins or so then into bed.
Books we read at any other time of day, he reads to himself for 20 min or so at morning WU before I get him up and always wants lots and lots of books read to him so he certainly loves them but it's not a BT thing for him and I can't force it unless one day he changes his mind, maybe when he's older.